Abstract:For a graph $G$, let $\lambda_1(G)$ and $\lambda_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $\lambda_1(G) + \lambda_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that attain the maximum/minimum. Moreover, for any $\alpha \in [0,1],$ we describe the extremal trees which maximize the convex combination $\alpha \lambda_1 + (1-\alpha)\lambda_2$ in the class of $n$-vertex trees for sufficiently large $n$.
From: Hitesh Kumar [view email]
[v1]
Thu, 15 Jan 2026 03:28:17 UTC (21 KB)
[v2]
Fri, 7 Aug 2026 05:42:06 UTC (26 KB)
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